Solve the formula Ax+By=C for y.

Answer:

$840.08

Step-by-step explanation:

18.14% is the same as 0.1814. If we put the value of the sale as x that means that 0.1814x=152.39. Dividing both sides by 0.1814 you get x is approx. $840.08.

Answer: [tex]\$840.08[/tex]

Step-by-step explanation:

You need to analize the information provided:

- The comission on each sale made by the salesman is 18.14%.

- On a particular sale the salesman makes a comission of $152.39.

Then, the amount of the sale represents the 100%

Let be "x" the amount of that particular sale. You can use this procedure to calculate it:

[tex]x=\frac{(\$152.39)(100\%)}{18.14\%}\\\\x=\$840.08[/tex]

Answer:

First problem: Solving for g.

[tex]g=27^{\frac{1}{x-2}}[/tex]

Second problem: Solving for x.

[tex]x=\log_g(27)+2[/tex]

Third problem: Assuming g is 9 while solving for x.

[tex]x=3.5[/tex]

Step-by-step explanation:

First problem: Solving for g.

[tex]g^{x-2}=27[/tex]

Raise both sides by 1/(x-2).

[tex](g^{x-2})^{\frac{1}{x-2}}=27^{\frac{1}{x-2}}[/tex]

[tex]g^{1}=27^{\frac{1}{x-2}}[/tex]

[tex]g=27^{\frac{1}{x-2}}[/tex]

Second problem: Solving for x.

[tex]g^{x-2}=27[/tex]

x is in the exponent so we have to convert to logarithm form since we desire to solve for it:

[tex]\log_g(27)=x-2[/tex]

Add 2 on both sides:

[tex]\log_g(27)+2=x[/tex]

[tex]x=\log_g(27)+2[/tex]

Third problem: Assuming g is 9 while solving for x.

[tex]9^{x-2}=27[/tex]

I'm going to solve this in a different way than I did above but you could solve it exactly the way I did for x when 9 was g.

I'm going to write both 9 and 27 as 3 to some power.

9=3^2 while 27=3^3.

[tex](3^2)^{x-2}=3^3[/tex]

[tex]3^{2x-4}=3^3[/tex]

Since both bases are the same on both sides, we need the exponents to be the same:

[tex]2x-4=3[/tex]

Add 4 on both sides:

[tex]2x=7[/tex]

Divide both sides by 2:

[tex]x=\frac{7}{2}[/tex]

[tex]x=3.5[/tex]

Now earlier for x in terms of g we got:

[tex]x=\log_g(27)+2[/tex]

I we input 9 in place of g and put it into our calculator or use some tricks without the calculator to compute we should get 3.5 as the answer like we did above when g was 9.

[tex]x=\log_9(27)+2[/tex]

[tex]x=\frac{3}{2}+2[/tex]

[tex]x=1.5+2[/tex]

[tex]x=3.5[/tex]

Answer:

a) negative

Step-by-step explanation:

When you multiply a given negative number by a positive number, the result becomes smaller than the original.

For instance let [tex]-100[/tex] be the original number.

Multiply by 2.

The result is -200

We know [tex]-200\:<\:-100[/tex]

The correct answer is A.

Answer: a) negative

Step-by-step explanation:

-100x2=-200

-200 is negative.

Step-by-step explanation:

let's Recall the properties of a parallelogram

1. the opposite sides of a parallelogram is congruent

AB=CD

8x-7=5x+2

8x-5x=7+2

3x=9

x=3

2. the consecutive angles are supplementary

angle A+angle D=180°

2y+50°+3y+40°=180°

5y+90°=180°

5y=90°

y=18

The circumference of a circle with an area of 50.3 m² is 25.12 m.

For example;

For example;

In this case;

The Area of a circle = 50.3 m²

π = 3.14

But; Area of a circle = πr²

Therefore;

3.14r²= 50.3 m²

r² = 50.3/3.14

   =16.019

r = √16.019

 = 4.0023

 ≈ 4.00

But;

Circumference of a circle is given by 2πr

Thus;

Circumference = 2 × 3.14 × 4.00

                          = 25.12 m

Keywords; Perimeter, Area, Area of a circle, Circumference of a circle

Level: Middle school

Subject; Mathematics

Topic: Area and Perimeter

Sub-topic: Area and circumference of a circle

Answer:

b + 15

Step-by-step explanation:

Let:

"boys" = b

"girls" = g = 15

Note that: "sum" = addition.

Combine:

b + 15 is your numerical expression of your question.

~

Answer:

1 to 15

Step-by-step explanation:

1 boy/ 15 girls

Answer:

A line that does not have an end to it.

Step-by-step explanation:

For example a line is forever, but if you put dots on the end, it will not be forever.

Answer:

A line segment is like a straight line, but has two dots on the edge of each end. A line segment has a starting and stopping point, which can help people tell the difference between other lines.

A line segment usually looks like this:

    \/   \/

 •----------•

Answer:

C. Reflection across the x-axis followed by the reflection across the y-axis.

Answer:

C

Step-by-step explanation:

Answer: 70

Step-by-step explanation:

Solve the equation in the innermost parentheses first that means solving 4+1 =5

The next step would be subtracting 9 from five which gives you 4

Next multiply 3 to 4 which gives you 12

Then multiply 5 with 12 which equals 60

Now you have the equation 60+20/4*2

Solve the division and multiplication part of the equation first because of the rule pemdas which shows multiplication comes before addition

First divide 20/4 which gives you 5 then multiply with 2 which gives you ten

After dividing and multiplying you are left with the equation 60+10

The answer is 70

Answer:

$132,612.50

Step-by-step explanation:

We will use the present value - future value formula. WHich is:

[tex]FV=PV(1+r)^t[/tex]

Where

FV is the future value (amount)

PV is the present value (amount)

r is the rate of interest (per year)

t is the number of years

In the problem given, the present amount (PV) is 125,000. The rate of interest (r) is 3%, or 0.03. And the time frame is 2 years, or t = 2.

Plugging these info in the equation, we can get the future value as shown:

[tex]FV=PV(1+r)^t\\FV=125,000(1+0.03)^2\\FV=125,000(1.03)^2\\FV=132,612.5[/tex]

This is the future vallue of $125,000 3% in 2 years.

Answer:

The answer is B) Medical Research

Step-by-step explanation:

Medical research is something typically done by private companies.

Answer: B. Medical research.

Step-by-step explanation: Public Health Programs: the types of public health programs that address STIs are: Prevention education, testing and counseling, and diagnosis and treatment.

:)

Answer:

y = - [tex]\frac{1}{4}[/tex] x² + 3

Step-by-step explanation:

Any point (x, y) on the parabola is equidistant from the focus and directrix.

Using the distance formula

[tex]\sqrt{(x-0)^2+(y-2)^2}[/tex] = | y - 4 |, that is

[tex]\sqrt{x^2+(y-2)^2}[/tex] = | y - 4 |

Squaring both sides

x² + (y - 2)² = (y - 4)² ← distribute parenthesis

x² + y² - 4y + 4 = y² - 8y + 16 ( subtract y² - 8y  from both sides )

x² + 4y + 4 = 16 ( subtract x² + 4 from both sides )

4y = - x² + 12 ( divide both sides by 4 )

y = - [tex]\frac{1}{4}[/tex] x² + 3

Answer:

same as him took test right

Step-by-step explanation:

Hey there!

Isolate the y variable by subtracting 12x in both sides:

-4y = -12x - 8

To solve for y divide -4 in both sides

y = 3x + 2

Our answer would be y = 3x + 2

Answer:

y = 3x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 12x - 4y = - 8 into this form

Subtract 12x from both sides

- 4y = - 12x - 8 ( divide all terms by - 4 )

y = 3x + 2 ← in slope- intercept form

Answer:

y = -3x+4

Step-by-step explanation:

Slope intercept form of a line is given by  y = mx + b

Where

m is the slope

b is the y intercept.

To find m, we need to take any arbitrary 2 points and see how many units up/down and how many units right/left we need to go from one to another. Basically change in y by change in x.

Let's take 2 arbitrary points: (0,4)  &  (2,-2)

So we need to go -6 units from y = 4 to y = -2. We need to go 2 units from x = 0 to x = 2.

Hence slope is change in y by change in x, which is -6/2 = -3

b is the y-interceept, the place where it cuts the y axis. Looking at the graph, it is at y = 4

Now we can write the equation as :

y = -3x+4

The question revolves around understanding the concepts of fixed costs, marginal costs, and economies of scale in the context of a computer manufacturing company. The company's ability to make substantial profits over a period of four years marks an effective management of these costs and leveraging economies of scale.

The computer company's scenario primarily involves understanding the concept of fixed costs and marginal costs in a business context. The fixed cost noted here is $250, which remains constant irrespective of the number of computers produced. The marginal cost, on the other hand, is variable depending on the volume of production.

For example, the company's marginal cost for producing computers is $700 for the first one, $250 for the second, and so on. The total cost is obtained by adding the fixed cost and the total variable (marginal) costs. Understanding these costs is critically important for the company to make decisions about pricing its products to achieve desired profit margins.

It means that if the company managed to make profits of $80 million after 4 years, they have effectively managed their fixed and variable costs and priced their computers profitably. In this example, by leveraging the economies of scale, that is, an advantage that companies gain when production becomes efficient with the increasing scale of output, the company has managed to reduce the average cost of production and increase profits.

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Answer:

The picture provided is the correct answer

Step-by-step explanation:

It needs to be greater than 4 or less than -4 in order for the absolute value to be greater than 7, so you're good.

Answer:

3x² – 5x + 10

Step-by-step explanation:

(4x² – 2x + 8) - (x² + 3x - 2) =

Drop the first set of parentheses because it is unnecessary.

= 4x² – 2x + 8 - (x² + 3x - 2)

To get rid of the second set of parentheses, change every sign inside.

= 4x² – 2x + 8 - x² - 3x + 2

Now, combine like terms.

= 3x² – 5x + 10

Answer:

3x^2 -5x +10

Step-by-step explanation:

(4x² – 2x + 8) - (x² + 3x - 2)

Distribute the negative sign

(4x² – 2x + 8) - x² - 3x + 2

I like to line them up vertically

4x² – 2x + 8

-x² - 3x  + 2

---------------------

3x^2 -5x +10

Answer:

The center is (5,0) and r=9.

Step-by-step explanation:

The standard form of a circle is [tex](x-h)^2+(y-k)^2[/tex] where (h,k) is the center and r is the radius.

On comparing your equation of

[tex](x - 5)^2 + (y-0)^2 = 9^2[/tex], we should see that h=5,k=0, and r=9.

The center is (5,0) and r=9.

Answer:

The center is at (5,0) and the radius is 9

Step-by-step explanation:

(x - 5)^2 + y^2 = 81.

An equation for a circle can be written in the form

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

Rewriting the equation

(x - 5)^2 + y^2 = 81.

(x - 5)^2 + (y-0)^2 = 9^2

The center is at (5,0) and the radius is 9

Answer:

2

Step-by-step explanation:

To find the slope of a line given two points [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex] you could use the formula: [tex]\frac{y_2-y_1}{x_2-x_1} \text{ or even } \frac{y_1-y_2}{x_1-x_2}[/tex].

However, what I'm fixing to do is equivalent to that except I think easier to remember.

You line up the points vertically and subtract, then put 2nd difference over 1st difference.

Like this:

 ( 3  ,   4)

- ( 5  ,   8)

---------------

-2        -4

So the slope is -4/-2=4/2=2.

The slope is 2.

Answer:

Step-by-step explanation: Sorry no time gtg : / (if you really need it I'LL ANSWER TOMMOROW

Answer:  The required simplified expression is -6xy.

Step-by-step explanation: We are given to simplify the following rational expression :

[tex]E=-\dfrac{18x^2y}{3x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following property of exponents :

[tex]\dfrac{z^a}{z^b}=z^{a-b}.[/tex]

From expression (i), we get

[tex]E\\\\\\=-\dfrac{18x^2y}{3x}\\\\\\=-\dfrac{18}{3}x^{2-1}y\\\\=-6xy.[/tex]

Thus, the required simplified expression is -6xy.

Answer:

(7, - 3 )

Step-by-step explanation:

Solve the 2 equations simultaneously to find intersection.

Given the equations of the sides

2x + 3y = 5 → (1)

3x + y = 18 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate the y- term

- 9x - 3y = - 54 → (3)

Add (1) and (3) term by term

(2x - 9x) + (3y - 3y) = (5 - 54) and simplifying gives

- 7x = - 49 ( divide both sides by - 7 )

x = 7

Substitute x = 7 into (1) or (2) for corresponding value of y

Substituting in (2)

21 + y = 18 ( subtract 21 from both sides )

y = - 3

Point of intersection = (7, - 3 )

Final Answer:

The coordinates of the intersection of the two lines are (x, y) = (7, -3).

Explanation:

To find the coordinates of the intersection of the two lines represented by the equations 2x + 3y = 5 and 3x + y = 18, we can solve this system of linear equations. Here's how to proceed step-by-step:
Step 1: Label the equations.
Let's call the first equation (1) and the second equation (2) for easy reference.
(1) 2x + 3y = 5
(2) 3x + y = 18
Step 2: Solve one of the equations for one of the variables.
Let's solve equation (2) for y:
y = 18 - 3x
Step 3: Substitute the expression for y in equation (1).
Now we substitute y in equation (1) with the expression we got from equation (2):
2x + 3(18 - 3x) = 5
Simplify the equation:
2x + 54 - 9x = 5
Combine like terms:
-7x + 54 = 5
Step 4: Simplify the equation for x.
Now we isolate x:
-7x = 5 - 54
-7x = -49
Divide both sides by -7 to find x:
x = -49 / -7
x = 7
Step 5: Substitute the value of x back into the equation for y.
We already have the expression for y from step 2 which was y = 18 - 3x. Now we substitute x = 7 into this expression to get y:
y = 18 - 3(7)
y = 18 - 21
y = -3
Step 6: State the coordinates of the intersection.
The coordinates of the intersection of the two lines are (x, y) = (7, -3).
Therefore, the vertex of the triangle at the intersection of the two graphs is at the point (7, -3).

Answer:

See attachment

Step-by-step explanation:

The mapping for a dilation with a scale factor k, about the origin is given by:

[tex](x,y) \to \: (kx,ky)[/tex]

From the graph, the coordinates of B are (1,1) and the scale factor is k=4.

We substitute into the rule to get

[tex]B(1,1) \to \: B'(4,4)[/tex]

The image of point B is plotted on the graph in the attachment.

To find the image of point B under a dilation with a scale factor of 4 about the origin (0,0), multiply the coordinates of point B by 4.

To plot the image of point B under a dilation with a scale factor of 4 about the origin (0,0), we need to multiply the coordinates of point B by the scale factor. If point B is represented as (x,y), then the image of B would be (4x, 4y).

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Answer:

The amount invested at 5.5% was $36,000 and the amount invested at 9% was $28,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x -----> the amount invested at 5.5%

(64,000-x) -----> the amount invested at 9%

in this problem we have

[tex]t=1\ years\\I=\$4,500\\ P=\$64,000\\r1=0.055\\P1=\$x\\P2=\$64,000-\$x\\r2=0.09[/tex]

so

[tex]I=P1(r1t)+P2(r2t)[/tex]

substitute the given values

[tex]4,500=x(0.055*1)+(64,000-x)(0.09*1)[/tex]

[tex]4,500=0.055x+5,760-0.09x[/tex]

[tex]0.09x-0.055x=5760-4,500[/tex]

[tex]0.035x=1,260[/tex]

[tex]x=\$36,000[/tex]

[tex]64,000-x=64,000-36,000=\$28,000[/tex]

therefore

The amount invested at 5.5% was $36,000 and the amount invested at 9% was $28,000

Answer:

[tex]\large\boxed{\sqrt{170}}[/tex]

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (9, 6) and (-4, 7). Substitute:

[tex]d=\sqrt{(-4-9)^2+(7-6)^2}=\sqrt{(-13)^2+1^2}=\sqrt{169+1}=\sqrt{170}[/tex]

The distance between the points (9,6) and (-4,7) can be found using the distance formula. By inputting the given coordinates into the formula, we find that the distance is √170 units.

The question is asking us to find the distance between two given points, (9,6) and (-4,7). In mathematics, this is commonly done using the distance formula: √[(x₂-x₁)² + (y₂-y₁)²]. Here, coordinates (x₁,y₁) are (9,6) and (x₂,y₂) are (-4,7).

Substituting these values into our formula, we have: Distance = √[(-4-9)² + (7-6)²] = √[(-13)² + 1²] = √[169 + 1] = √170.

Therefore, the distance between the points (9,6) and (-4,7) is √170 units.

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Answer:

30 each of 23% bars and 18 each of 79% bars

Step-by-step explanation:

If x is the number of 1 kg 23% copper bars, and y is the number of 1 kg 79% copper bars, then:

x + y = 48

0.23x + 0.79y = 0.44(48)

Substituting and solving:

0.23x + 0.79(48-x) = 0.44(48)

0.23x + 37.92 - 0.79x = 21.12

16.8 = 0.56x

x = 30

y = 48 - x

y = 18

You need 30 each of 23% bars and 18 each of 79% bars.

Answer:

x1 = 2.79129, x2 = 1.79129

Step-by-step explanation:

x^2-5-x

x^2-5+x=0

x^2+x-5=0

-1+-square root od=f 1^2 - 4x1x(-5) / 2x1  = -1+- square root of 21 (add numbers together) / 2

then solve the formula with a plus sign instead of +- then and solve the formula with a - this time and you should get x1 = 2.79129, x2 = 1.79129, or -1 +square root of 21 (add numbers together) / 2 and -1 - square root of 21 (add numbers together) / 2

For this case we must solve the following equation:

[tex]x ^ 2 = 5-x[/tex]

By manipulating algebraically we have:

[tex]x ^ 2 + x-5 = 0[/tex]

The quadratic formula is given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

We have to:

[tex]a = 1\\b = 1\\c = -5[/tex]

Substituting we have:

[tex]x = \frac {-1 \pm \sqrt {1 ^ 2-4 (1) (- 5)}} {2 (1)}\\x = \frac {-1 \pm \sqrt {1 + 20}} {2}\\x = \frac {-1 \pm \sqrt {21}} {2}[/tex]

So, we have two roots:

[tex]x_ {1} = \frac {-1+ \sqrt {21}} {2} = 1,7913\\x_ {2} = \frac {-1- \sqrt {21}} {2} = - 2.7913[/tex]

Answer:

[tex]x_ {1} = \frac {-1+ \sqrt {21}} {2}\\x_ {2} = \frac {-1- \sqrt {21}} {2}[/tex]

The slope of the line is the change in the Y values over the change in X values.

Using the given points (2,-5) and (-2,3)

The Y values are -5 and 3 and the X values are 2 and -2.

The slope = (3 - (-5)) / -2 - 2) = 8/-4 = -2

The slope is -2

Answer:

could it be letter H? please lmk

Answer:

16

Step-by-step explanation:

You can choose

In total there are

[tex]2\cdot 2\cdot 4=16[/tex]

different outfits.

Another way to solve this problem is simply count all outfits:

Shirts [tex]Sh_1, \ Sh_2[/tex]

Pants [tex]P_1,\ P_2[/tex]

Shoes [tex]S_1, \ S_2,\ S_3,\ S_4[/tex]

All outfits

[tex]Sh_1P_1S_1, \\ Sh_1P_1S_2, \\ Sh_1P_1S_3, \\ Sh_1P_1S_4, \\ Sh_1P_2S_1, \\ Sh_1P_2S_2, \\ Sh_1P_2S_3, \\ Sh_1P_2S_4, \\ Sh_2P_1S_1, \\ Sh_2P_1S_2, \\ Sh_2P_1S_3, \\ Sh_2P_1S_4, \\ Sh_2P_2S_1, \\ Sh_2P_2S_2, \\ Sh_2P_2S_3, \\ Sh_2P_2S_4[/tex]